The aim of this paper is to generalize the results in [1] and [13]. Here, we are interested in two problems concerning certain classes of near rings satisfying one of the following polynomials identities :(∗) For each x; y in a near-ring N, there exist positive integers t = (x; y) ≥ 1 and s = s (x; y) > 1 such that xy = ±ysxt.(∗∗) For each x; y in a near-ring N, there exist positive integers t = t (x; y) ≥ 1 and s = s (x; y) > 1 such that xy = ±xtys.